Typical solid electrolyte fuel cells require a time to raise their temperatures at cold start. Conventional fuel cell systems have therefore been mainly used as a stationary type, which is not frequently cold-started. There are, however, many demands for applying fuel cell systems to mobile objects such as vehicles. Patent Literature 1 proposes a multi-stage fuel cell stack including a small fuel cell stack and a large fuel cell stack to achieve both fast start-up and large output required by a mobile object.